Don't override HealthCheckService log levels

[emlautarom1]

Fixes #6017

Changes

• Don't override HealthCheckService log levels

Types of changes

What types of changes does your code introduce?

• Bugfix (a non-breaking change that fixes an issue)
• New feature (a non-breaking change that adds functionality)
• Breaking change (a change that causes existing functionality not to work as expected)
• Optimization
• Refactoring
• Documentation update
• Build-related changes
• Other: Description

Testing

Requires testing

• Yes
• No

If yes, did you write tests?

• Yes
• No

Documentation

Requires documentation update

• Yes
• No

Requires explanation in Release Notes

• Yes
• No

Remarks

Similar to #6097. We missed an extra rule related to JSON Web API Health Checks, so we're adding it here.